"The Senate Republican establishment betrayed the grassroots and recruited Democrats in Mississippi to defeat Chris McDaniel," the SCF petition said . "Fight back by pledging not to donate to the National Republican Senatorial Committee."

Cochran finished behind McDaniel in the June 3 primary, but the senator came back to win the runoff three weeks later. To do this, Cochran's campaign and allies overtly recruited black voters — a traditionally reliable Democratic voting block in Mississippi — in the second match-up.

Back on Capitol Hill, the SCF's response to the race could get awkward for Cruz. He continues to serve as vice chairman for grass-roots outreach at the NRSC and previously pledged not to work to oust any GOP incumbent in the Senate.

But the Texas Republican supported the SCF's efforts in the past. He made an appearance in a recent SCF television ad to boost former Oklahoma Speaker of the House T.W. Shannon. Rep. James Lankford defeated Shannon in a GOP primary for Sen. Tom Coburn's seat, which is open because the Oklahoma Republican is resigning at the end of this Congress.

Multiple queries to Cruz's office Sunday and Monday asking if he would disavow the SCF's effort to defund the NRSC yielded no response from the senator.

"Majority-Leader-Wannabe Mitch McConnell, NRSC Chairman Jerry Moran, and the others who supported Thad Cochran's disgraceful attacks on Chris McDaniel are part of the problem," SCF President Ken Cuccinelli said in a message to supporters. "These politicians don't believe in the principles of freedom that make America great. Their ideology is power and they will do anything to keep it."

Last October, the tension between Cruz's role at the NRSC and his backing of the SCF campaigns was apparent when the SCF endorsed Matt Bevin in the Kentucky Republican primary against Minority Leader Mitch McConnell.